Preheat the oven to 180 C / Gas 4. Line a 20x30cm baking tin with tin foil leaving a good amount of overhang over the sides.
Place 300g of strawberries in a food processor and blend until smooth. Press through a sieve into a clean saucepan. Dissolve the cornflour in a little cold water then add to the strawberry purée. Cook and stir for 8 to 10 minutes over a low heat until thickened. Remove from the heat and allow to cool.
Combine the crushed digestives and butter in small bowl and mix well. Press evenly into the bottom of the prepared baking tin.
In large bowl, beat the cream cheese until fluffy. Gradually beat in condensed milk until smooth. Add eggs, lemon juice and vanilla; mix until thick and creamy. Pour over prepared base.
Drop the strawberry purée mixture by spoonfuls over the cheesecake. Gently swirl with a knife to create a marbled effect.
Bake 25 to 30 minutes until centre is set. Remove from the oven and allow to cool slowly and completely for at least 3 to 4 hours. Cut into slices or squares and serve.